package 递归回溯.二维版;

public class No36有效的数独 {

    /**
     * 判断一个 9x9 的数独是否有效。只需要根据以下规则，验证已经填入的数字是否有效即可。
     * 数字 1-9 在每一行只能出现一次。
     * 数字 1-9 在每一列只能出现一次。
     * 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。
     * 上图是一个部分填充的有效的数独。
     * 数独部分空格内已填入了数字，空白格用 '.' 表示。
     *
     * 示例 1:
     * 输入:
     * [
     *   ["5","3",".",".","7",".",".",".","."],
     *   ["6",".",".","1","9","5",".",".","."],
     *   [".","9","8",".",".",".",".","6","."],
     *   ["8",".",".",".","6",".",".",".","3"],
     *   ["4",".",".","8",".","3",".",".","1"],
     *   ["7",".",".",".","2",".",".",".","6"],
     *   [".","6",".",".",".",".","2","8","."],
     *   [".",".",".","4","1","9",".",".","5"],
     *   [".",".",".",".","8",".",".","7","9"]
     * ]
     * 输出: true
     */

    private boolean[][] row=new boolean[9][9];
    private boolean[][] col=new boolean[9][9];
    private boolean[][] box=new boolean[9][9];

    public boolean isValidSudoku(char[][] board) {

        for (int i = 0; i < 9; i++) {
            for (int j = 0; j < 9; j++) {
                if(board[i][j]!='.'){
                    //是数字就需要验证
                    int num=board[i][j]-'1';
                    int boxIndex=i/3+(j/3)*3;
                    if(row[i][num]||col[j][num]||box[boxIndex][num])
                        return false;
                    row[i][num]=true;
                    col[j][num]=true;
                    box[boxIndex][num]=true;
                }
            }
        }

        return true;
    }

}
